Abstract
High-resolution numerical simulations were performed to study the structure and substructure of Milky Way- and cluster-sized halos in a Lambda CDM cosmology with self-interacting (SI) dark particles, where the particle cross section, sigma_{{DM}}() , is assumed constant or inversely proportional to the relative velocity. We conclude that the cuspy halo problem at galaxy scales of the Lambda CDM cosmogony can be solved in the latter case. At the same time, the subhalo population remains roughly similar to that seen on CDM halos.